Paralax mapping in Cycles
Alright, lets go over this. 

Firstoff, the surface albedo (color). You got that one, just straight into the color. 

Onto the roughness. Roughness maps are black and white. You've already set your image texture to "Non Color Data", however I'd recommend feeding it through a color ramp. This does not only allow you more control over the actual texture but also elminiates any residual color. Personally I don't know if blender converts the greyscale-map into data before moving ahead or if it preserves color, since normal maps are colored based. 

I'd remove the "Invert" node, it does weird things to the values (I've not once used to great success). You can achieve the same result with a color ramp, with more control over it. 

So, the normal map. Let me go on a bit of tangent here about bump maps as well, since you used a bump node.

A bump map is a very simple way of non-destructive displacement in which a greyscale map controls light behavior. It is based on a few tricks of human perception. However it does not include any actual data on simulated geometry. 

This is where normal maps come into play. It gives a more detailed description of how the light is supposed to interact with the surface, which is why it is that nifty shade of pink. Different colors correspond to different geometry directions. 

We could move on to vector displacement maps here, but that's quite a way ahead. 

Back to your node setup then! With the theory covered, how does one implement that? You've nearly got the implementation down here. Since a normal map uses colors and not a greyscale you're going to need the normal-map node (as you have rightly done). Connect it to the Normal input of the Principled BSDF shader and there you go! Don't forget to set the normal maps texture node to "Non Color Data" for it to work properly! This is because you're not taking color data from the texutre map, but rather geometry data. 

Just as a heads-up, specular differes from roughness. You can use the it as a roughness map here, which is great, however specular is a different kind of workflow compared to roughness.